Literally all of that is categorically untrue and its incredible the same inaccuracies about the Hungarian revolution get spread in left circles 70 years after it. The revolution was led by Leninists. There is no evidence of fascist agitation in the fighters. The best you can find is some Horthy era officials that were in prison got released along with everyone else (and if you say Béla Király was fascist agitation, then you'll need to explain how that was true as he joined the Hungarian Communist Party in 1945 when he returned from the USSR, was promoted to general then director of the Miklós Zrinyi military academy in 1950, until the 1951 purge. He was certainly a Hungarian nationalist, and his men killed many Rakosi officials that they should not have, but not a fascist agitator. You'll also have to explain why Rakosi vouched for him and other army officials. Furthermore, there were still far more people involved in the workers councils than any of those army officials groups). The relationship of the Hungarian army and national guard, and which sides defected to who, and how that all intertwined with the worker uprisings is very complicated. The Hungarians were under extreme pressure from the soviets to accuse Nagy and others rebelling of being imperialists and fascists etc because of how embarrassing it was that fellow Leninists led the uprising. Communist worker councils had the country in a standstill for weeks with strikes even after the fighting ended. You can read declassified CIA cables from the period and they are completely shocked the revolution happened and taken by surprise and have no idea what to do because the actual fascists they did try and help post WW2 were already detained or dead. They literally had a single CIA officer in Hungary in 1956, and he didn't even do anything lol. Cables also show that in the case of Hungary, the CIA did not supply any material support. The groups they tried to fund were destroyed by 1953. The cables literally lament the fact that they don't have anyone to back.. Radio Free Europe was certainly propagandizing claiming there was US and UN support coming, but in actuality it was not and was never coming. Eisenhower was completely focused on the Suez crisis and basically ignored Hungary. RFE was even trying to appeal to insurgents (which were a combination of communists and anti-communists) at the same time as decrying and demanding Nagy step down, totally incoherent.

I mean come on Lukacs and his daughter were prominent in the uprising. The majority makeup of Nagy's government were Leninists. The initial protests were pushed by university students and leftist intellectuals (see the writers union speech outlining the principle socialist demands of the protests here and here. Hell if you want to go on the authority of Tito, he was demanding Nagy and other revolutionaries be given safe passage to Yugoslavia and only gave in to the USSR after a series of phone calls directly with Khrushchev. You can see excerpts of his speech here.

This is what was demanded and cheered on by hundreds of thousands of people protesting in Budapest (hours after which the tanks were rolled in):

PETOFI CIRCLE'S TEN DEMANDS.

BUDAPEST

The leadership of the Petofi Circle has passed the following resolution at its meeting:

1. In view of the present situation in Hungary we propose that the Central Committee of the Workers' [Communist] Party should be convened with the minimum possible delay. Comrade Imre Nagy should take part in the preparatory work of this session.

2. We consider it necessary that the Party and Government should reveal the country's economic situation in all sincerity, revise the second Five-Year Plan directives, and work out a specific constructive program in accordance with our special Hungarian conditions.

3. The Central Committee and the Government should adopt every method possible to ensure the development of socialist democracy, by specifying the real functions of the Party, asserting the legitimate aspirations of the working class and by introducing factory self-administration and workers' democracy.

4. To ensure the prestige of the Party and of the state administration, we propose that Comrade Imre Nagy and other comrades who fought for socialist democracy and Leninist principles should occupy a worthy place in the direction of the Party and the Government.

5. We propose the expulsion of Matyas Rakosi from the Party Central Committee and his recall from the National Assembly and the Presidential Council. The Central Committee, which wishes to establish calm in the country, must offset present attempts at a Stalinist and Rakosiite restoration.

6. We propose that the case of Mihaly Farkas be tried in public in accordance with socialist legality.

7. The Central Committee should revise resolutions it passed in the period which has just elapsed -resolutions which have proved wrong and sectarian- above all the resolutions of March 1955, the December 1955 resolution on literature, and the 30 June 1956 resolution on the Petofi Circle. We propose that the Central Committee should annul these resolutions and draw the proper conclusions as to the persons concerned.

8. Even the most delicate questions must be made public, including the balance sheets of our foreign trade agreements and the plans for Hungarian uranium.

9. To consolidate Hungarian-Soviet friendship, let us establish even closer relations with the Soviet Party, State and people, on the basis of the Leninist principle of complete equality.

10. We demand that at its meeting on 23 October the DISZ Central Committee should declare its stand on the points of this resolution and adopt a resolution for the democratisation of the Hungarian Youth Movement.

Now there was violence against communist party members, and a lot of it, but by both other communists as local party centers dissolved and were taken over by workers councils and state police who defected and by rightist national guard defextors. Many local party figures also joined the councils.

There was no mass anti-semitic violence (see here and here for what documentation there is), at best there were sporadic incidents in the countryside. Many of the militia leaders backing the workers councils were Jewish. The accusations in the Aptheker book are totally unsubstantiated and it is a tragedy of scholarship that he wrote it, it pales in comparison to his other work. He wrote it using extremely biased reports given to CPUSA that did not reflect what was actually happening. What he is actually referring to is that in the countryside where general anti-communist sentiment was higher, and anti-semiticism was higher, there were executions of commuinst officials who were more likely to be Jewish, however these incidents were isolated and in no way reflect the actual character of the uprising. Péter Nádas, the great gay Jewish socialist Hungarian writer, lived through the revolution as a teenager and celebrates its character.

Here's a great account of British Communist Party journalist who was on the ground for the whole revolution (and whose account of it got him kicked out of the party because he refused to censor it as it went against the line of the USSR on it). It of course also suffers from inaccuracies of the time (for example it reports that 2000 emigres from Austria armed with American weapons came over the border to agitate, there's no evidence this ever happened).

If you want some really good modern scholarship on worker movements in Hungary, I'd check out the work of the late Mark Pittaway, specifically this essay collection or his book The Workers State to get a better idea of the complex interactions of workers from below (by far the biggest portion of agitation that continues long after the end of the fighting), Nagy's government, and the left and right insurgents.